1. ## Integration/Derivative problem

The Acceleration of an object is given by a(t)=6sin(t) with initial velocity of -9.5(v(0) = -9.5). Find the distance the object travels on the interval [0,pi] to the nearest integer.

I was able to take the integral of the acceleration to get it to the velocity and I found C(the number that when you take the integral it ends up at the end) but I am not sure how to continue. I assume you take another integral but I am not sure.

2. Originally Posted by CalcGeek31
The Acceleration of an object is given by a(t)=6sin(t) with initial velocity of -9.5(v(0) = -9.5). Find the distance the object travels on the interval [0,pi] to the nearest integer.

I was able to take the integral of the acceleration to get it to the velocity and I found C(the number that when you take the integral it ends up at the end) but I am not sure how to continue. I assume you take another integral but I am not sure.

After you found C, you were able to obtain $v(t)$. Now, you need to find $\int_0^\pi v\left(t\right)\,dt$.

Can you take it from here?

3. s = v*t
if v (= velocity) is constant.

s = v1*delta_t1 + v2*delta_t2 + ...
where v1 is constans during the timeinterval delta_t1

s = integral(t_ini to t_fin) v(t)*dt
if the velocity is a function in t.

So, you're right!

4. I believe I can but I was wondering if my velocity function was correct I apologize for not mentioning it originally,

I got $v(t)= -6cos(t) - 3.5$

5. Originally Posted by CalcGeek31
I believe I can but I was wondering if my velocity function was correct I apologize for not mentioning it originally,

I got $v(t)= -6cos(t) - 3.5$
Correct.